Sample GCSE Maths Question - Cricket Based

Recently we did a practice GCSE statistics paper at school, and here is the question everyone got wrong:

Freddie has 10 innings during the cricket season.

His scores were as follows:

0, 12, 65, 74, 34, 125, 98, 4, 6, 36

Q1: What was his median score?
Q2: What was the range of his scores?
Q3: Which type of average is best suited to the data? Median (Middle No.), Mode (No. that appears most) or Mean (sum of data divided by how many pieces of data)

Q1 and 2 are straightfoward, nearly everyone got them right.

But almost everyone got Q3 wrong, as the answer was median and not mean.

This means that according to the marker, the best way to work out a batting average is to line up all the scores low to high and pick the middle number, not the mean which is a normal cricket average.

Two points: I wrote mean as soon as I had read the question, as it is common knowledge a batting average is runs/times out. The only people who got it right had no knowledge of cricket averages at all. Surely the majority of the world (the cricket community) is right?

And in the possibility of a median average being the correct answer, why do we use the mean instead of the median. (Form, year by year analysis, accuracy, fluctuating numbers)

For example:

Smiths 'median average' is 50. In his next four innings he scores: 300, 200, 35 and 40, yet as the 50 will still be the middle number, his 'median' does not change.

That question is rubbish, I can't believe they would set a question like that without considering the fact that cricket averages are worked out in a completely different way. It's a bit harsh on you guys.

That's fantastic. 150 years of cricket statistics and the GCSE board comes up and tells us we've been doing it wrong all along.

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Member of JMAS, DMAS, FRAS and RTDAS

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Keith Pont, the former Essex allrounder (don't let his averages deceive you, he was a much better player than they suggest), was director of development for the ECB and one of his ideas was to get cricket into classrooms via just this sort of thing, so obviously his ideas have been implemented even if wrongly!

A high mean is obviously necessary but a player X with slightly lower mean than player Y but with a lower SD (showing more consistency) would surely be more acceptable.

So in judging players in the real sense SD has to be tabulated as well.

Now to tabulate the SD, do we exclude the extreme scores as a 400 is a good score but adverse the SD adversely? Maybe if a player plays 100 completed innings, the 5 lowest and 5 highest scores can be excluded.

IMDB user rating excludes some extremes - as claimed in their site. They claim its the way statistics do it as well.

I am not a statistician but are there some ways to do it in computing the SD?

Of course there are many many other variables which make judging players comparatively so difficult.

Ignoring the fact that they got the answer wrong, question 3 is awful anyway - especially as if it does actually tells you what mode, mean etc. actually are (ignore this if you've just added the description in yourself), just after a question that says "What was his median score?"